A small copy center uses 4 550-sheet boxes of copy paper a week. Experience sugg
ID: 328600 • Letter: A
Question
A small copy center uses 4 550-sheet boxes of copy paper a week. Experience suggests that usage can be well approximated by a normal distribution with a mean of 4 boxes per week and a standard deviation of 40 boxes per week. 3 weeks are required to fill an order for letterhead stationery. Ordering cost is $4, and annual holding cost is 33 cents per box. Use Table a. Determine the economic order quantity, assuming a 52-week year (Round your answer to the nearest whole number.) EOQ boxes b. If the copy center reorders when the supply on hand is 13 boxes, compute the risk of a stockout. (Round "z" value to 2 decimal places and final answer to 4 decimal places.) Risk c. If a fixed interval of 5 weeks is used for ordering instead of an ROP, how many boxes should be ordered if there are currently 23 boxes on hand, and an acceptable stockout risk for the order cycle is .0228? (Round "z" value to 2 decimal places and final answer to the nearest whole number.) 0Explanation / Answer
Annual demand of boxes of copy paper = D = 4 / week x 52 weeks = 208 boxes
Ordering cost = Co = $ 4
Annual unit holding cost = Ch = $ 0.33 per box
Therefore ,
Economic Order Quantity ( EOQ )
= Square root ( 2 x Co x D / Ch)
=Square root ( 2 x 4 x 208 / 0.33)
= 71 ( rounded to nearest whole number )
EOQ = 71 BOXES
Given are following details :
Weekly demand = d = 4 boxes
Lead time ( time to fill an order ) = L = 3 weeks
Standard deviation of weekly demand = d = 0.40 boxes
It is to be noted :
Reorder point = Weekly demand x Lead time + Safety stock = d x L + Z value of in stock probability x Standard deviation of daily demand
Since , reorder point = 13 boxes ,
13 = 4 x 3 + z x 0.40
Or, 0.40.Z = 1
Or, Z = 2.5
Corresponding in stock probability for Z = 2.5 as derived from standard normal distribution table = 0.99379
Therefore, risk of stock out = 1 – in stock probability = 1 – 0.99379 = 0.0062 ( rounded to 4 decimal places )
RISK = 0.0062
Given ,
Order interval = 5 weeks
Lead time = 3 weeks
Therefore , Protection period = Order interval + Lead time = 5 + 3 = 8 weeks
Stockout risk = 0.0228
Therefore , In stock probability = 1 – 0.0228 = 0.9772
Z value for in stock probability 0.9772 = NORMSINV ( 0.9772 ) = 1.999
Standard deviation of demand during protection period
= Standard deviation of weekly demand x Square root ( Protection period )
= 0.40 x Square root ( 8 )
= 0.4 x 2.828
= 1.131
Therefore , Safety stock = Z value x Standard deviation of demand during protection period = 1.999 x 1.131 = 2.260 ,
Number of boxes to be ordered with 23 boxes on hand
= Average weekly demand x Protection period + Safety stock – 23
= 4 x 8 + 2.26 – 23
= 34.26 – 23
= 11.26 ( 11 rounded to nearest whole number )
11 BOXES SHOULD BE ORDERED
EOQ = 71 BOXES